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You are in a land where there are only knights and knaves. Knights always tell the truth and knaves always lie. You come across three inhabitants of this land who are out on a boat off shore. It’s dark and you can’t tell who is who so you shout out to them, "Which one of you is a knight and which one is a knave?" The first one says something, but the wind comes up and you can’t hear what they said. The second one then says, "She said she’s an knight, and so am I." The third one says, "They’re both lying; I’m an knight and they’re both knaves." Who is a knight and who is a knave? For full credit, you must explain/prove your answer.

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vaughnjustin649

Answer:

The first two are Knights

Explanation:

Assume A is a knave. In that case, she is lying. B’s statement is then a contradiction because a knight could never say “If she is lying (she is), then I am a knave,” because that would be a lie. Similarly, if B was a knave, B would never say, “If she is lying (she is), then I am a knave,” because that would be the truth. So if A is a knave, B cannot be a knight or a knave, which is a contradiction. Therefore, A cannot be a knave. Because A cannot be a knave, A must be a knight. In that case, she is not lying. B’s statement is then vacuously true. Therefore, B must be a knight, since a knave cannot make a true statement.

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